This section is dedicated to studying the effect of \(k\) , and thus the influence of domain size \([0,2 \pi /k]\)  on the TWs.
Figure REF  shows how a single branch of travelling waves at \(Re = 30\)  (purple in Figure REF ) changes with \(k\) .
It has already been established that the steady arrowhead structure is highly sensitive to domain length in the EIT regime [1]}. There, through capturing larger scale motions, an increase in domain length was found to unveil structures of increasing complexity, with the possibility of inducing chaotic dynamics at certain parameter combinations.
Similar tendencies can be observed in our case (cf. Figure REF ): An increase in \(k\)  (and thus decrease in domain length)
has a considerable weakening effect on the arrowhead structure,
eventually resulting in a complete eradication of TWs
and a subsequent relaminarization. Despite this observation, the location of the saddle-node points seems largely unaffected by \(k\)  (cf. Figure REF ), making the marked 'nonlinearly unstable' region on Figure REF  robust to changes in the assumed periodicity and domain size.
